{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequentism, Samples, and the Bootstrap."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "New Latex commands are defined here. Doubleclick to see.\n",
    "\n",
    "$\\newcommand{\\Ex}{\\mathbb{E}}$\n",
    "$\\newcommand{\\Var}{\\mathrm{Var}}$\n",
    "$\\newcommand{\\Cov}{\\mathrm{Cov}}$\n",
    "$\\newcommand{\\SampleAvg}{\\frac{1}{N({S})} \\sum_{s \\in {S}}}$\n",
    "$\\newcommand{\\indic}{\\mathbb{1}}$\n",
    "$\\newcommand{\\avg}{\\overline}$\n",
    "$\\newcommand{\\est}{\\hat}$\n",
    "$\\newcommand{\\trueval}[1]{#1^{*}}$\n",
    "$\\newcommand{\\Gam}[1]{\\mathrm{Gamma}#1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# The %... is an iPython thing, and is not part of the Python language.\n",
    "# In this case we're just telling the plotting library to draw things on\n",
    "# the notebook, instead of on a separate window.\n",
    "%matplotlib inline\n",
    "# See all the \"as ...\" contructs? They're just aliasing the package names.\n",
    "# That way we can call methods like plt.plot() instead of matplotlib.pyplot.plot().\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import time\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DATA AND MODELS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why do we do this? Lets get some data...\n",
    "\n",
    "Forty-four babies -- a new record -- were born in one 24-hour period at\n",
    "the Mater Mothers' Hospital in Brisbane, Queensland, Australia, on\n",
    "December 18, 1997.  For each of the 44 babies, _The Sunday Mail_\n",
    "recorded the time of birth, the sex of the child, and the birth weight\n",
    "in grams. Also included is the number of minutes since midnight for\n",
    "each birth.\n",
    "\n",
    "REFERENCE:\n",
    "Steele, S. (December 21, 1997), \"Babies by the Dozen for Christmas:\n",
    "24-Hour Baby Boom,\" _The Sunday Mail_ (Brisbane), p. 7.\n",
    "\n",
    "\"Datasets\n",
    "and Stories\" article \"A Simple Dataset for Demonstrating Common\n",
    "Distributions\" in the _Journal of Statistics Education_ (Dunn 1999).\n",
    "\n",
    "Columns\n",
    "\n",
    "       1 -  8  Time of birth recorded on the 24-hour clock\n",
    "       9 - 16  Sex of the child (1 = girl, 2 = boy)\n",
    "      17 - 24  Birth weight in grams\n",
    "      25 - 32  Number of minutes after midnight of each birth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>24hrtime</th>\n",
       "      <th>sex</th>\n",
       "      <th>weight</th>\n",
       "      <th>minutes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>3837</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>104</td>\n",
       "      <td>1</td>\n",
       "      <td>3334</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>118</td>\n",
       "      <td>2</td>\n",
       "      <td>3554</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>155</td>\n",
       "      <td>2</td>\n",
       "      <td>3838</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>257</td>\n",
       "      <td>2</td>\n",
       "      <td>3625</td>\n",
       "      <td>177</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   24hrtime  sex  weight  minutes\n",
       "0         5    1    3837        5\n",
       "1       104    1    3334       64\n",
       "2       118    2    3554       78\n",
       "3       155    2    3838      115\n",
       "4       257    2    3625      177"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_table(\"babyboom.dat.txt\", header=None, sep='\\s+', \n",
    "                   names=['24hrtime','sex','weight','minutes'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "788.7272727272727"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.minutes.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is data?\n",
    "\n",
    "In labs before, you have seen datasets. As so in the example above. You have seen probability distributions of this data. Calculated means. Calculated standard deviations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Pandas code for the week\n",
    "\n",
    "We'll keep showing some different aspects of Pandas+Seaborn each week. For example, you can very easily calculate correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>24hrtime</th>\n",
       "      <th>sex</th>\n",
       "      <th>weight</th>\n",
       "      <th>minutes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>24hrtime</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.028027</td>\n",
       "      <td>0.075636</td>\n",
       "      <td>0.999840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <td>0.028027</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.228751</td>\n",
       "      <td>0.031815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weight</th>\n",
       "      <td>0.075636</td>\n",
       "      <td>0.228751</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.079616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>minutes</th>\n",
       "      <td>0.999840</td>\n",
       "      <td>0.031815</td>\n",
       "      <td>0.079616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          24hrtime       sex    weight   minutes\n",
       "24hrtime  1.000000  0.028027  0.075636  0.999840\n",
       "sex       0.028027  1.000000  0.228751  0.031815\n",
       "weight    0.075636  0.228751  1.000000  0.079616\n",
       "minutes   0.999840  0.031815  0.079616  1.000000"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember that this correlation is a statistic calculated only on this data...this sample of babies. I have not asked the question: what does this mean for the population of babies.\n",
    "\n",
    "I'd thought that there would be a greater correlation between weight and sex, but apparently its not at all big for babies. Telles you Idont know much about babies :-). Here's a plot more tohelp you in future homework:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x10bfe4110>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WlkaWZbF48eL42te+FiUlJXHSSSc1/O7WbvMV6m2E191tVVlZGRs2\nbIgvfOELjf5Bb922jq31N6LjrV0zTn7MOPkx4+TLjJMfM07bMOfkpyPPODsV+0u8P5l6rzfffDPe\neuutePXVV+MrX/lKlJaWxq9//euYMGFCRESMHTs21q5dG926ddvsvt27d48333wzIt59J6J79+6b\n7dOtW7dYu3ZtsaVuF2bNmhXz5s2Lr3/967FmzZrYeeedY6edGv/v6t69e0Nf9Ld47+3t0qVLrd1W\nMm3atJg6dWpERFxyySVRVlYWc+bMsXZbwZZ663V327z88stx++23x4wZM6JLly6NbvOau+2a6m9H\nXLtmnLZlxsmPGScfZpz8mHHyYc7JT0efcYoOeJrSq1evmD59ehxwwAGx5557RkTEqFGjYunSpTFt\n2rQYO3ZsZFkWJSUlW7x/p07vnkjU1D5b2749euCBB+Laa6+N4447Ls4888y47bbbtql3+vv/Hnjg\ngZg4cWJDb9955x1rt5Uce+yxcdhhh8VTTz0V06ZNi7q6uujatau12wq21Nvzzz/f2m2hjRs3xlVX\nXRWnnnpqDB06NCIa/67b2rcdubcRhfub2syQWr0dnRknP2ac/Jhx8mPGaX3mnPykMOO0SsCzyy67\nxKhRozbbfsQRR8QTTzwR69atix49emwxbVq7dm307NkzIiJ69OgRNTU1Te6zvZs+fXrccMMN8fGP\nfzxuvPHGiIjo2bNn1NXVxYYNG6Jz584N+76/d/rbtC311tptPeXl5RERMWLEiFi7dm388Ic/jMsu\nu8zabQVb6u2FF15o7bbQzJkzY8mSJVFZWRn19fUR8e4f0izLor6+3mvuNmqqvxs2bEjudTe1ejsy\nM05+zDj5MuPkx4zT+sw5+Ulhxin6GjxNeeWVV+KnP/1pw0WxNnnnnXdi1113jW7dukVZWVnU1NRs\nts9rr70WAwYMiIh3Lwq3ePHiRrdv3LgxXn/99YZ9tmc333xzXH/99TF27Ni45ZZbGk6b22effSLL\nsnjttdca7f/+3unv1m2tt9butqmpqYn77rtvsxepioqKqKura/hstbXbfIV6+5e//MXabaFHHnkk\nlixZEiNHjoxBgwbFoEGDoqqqKmbPnh2DBg2KLl26WLfboKn+HnjggVFdXZ3U2vV3onWYcfJjxsmH\nGSc/Zpx8mXPyk8KM0yoBz5IlS+K6666Lxx9/vGFblmXx0EMPxcEHHxwR756atGHDhnj00Ucb9qmu\nro6XXnqpIeUaNWpULFu2LJ5//vmGff70pz/FmjVrtpiEbU9mzJgRd9xxR4wfPz4mTZrUcHpWRMSw\nYcNil112iYcffrhh28qVK+PPf/5zo97p75Y11Vtrd9usXLkyrrrqqpgzZ06j7X/84x+jd+/e8YlP\nfMLabaFCva2vr7d2W+i6666L++67r+Hn3nvvjbKyshg9enTcd999ccIJJ1i326BQf1977bWk1q6/\nE9vOjJMfM05+zDj5MePky5yTnxRmnFb5iNahhx4aw4YNi2uvvTZWrlwZvXv3jl/84hfx4osvxj33\n3BMR716l+7jjjmu4oF7Pnj3j5ptvjoqKivjEJz7R8IsMHTo0LrroovjqV78a69evj+uvvz6OPvro\n+MhHPtIapXZIS5cujRtvvDEOOOCAOOGEE+LZZ59tdPvgwYPjrLPOismTJ0enTp1in332idtuuy1K\nS0vj1FNPjQj93ZpCvT344IOt3W2w7777xpgxY+L666+P9evXR//+/eOhhx6KBx54ICZNmhQ9evSw\ndluoUG8POeQQa7eFtvTOxy677BK9evWKAw88MCLCut0Ghfq7cePGpNauGWfbmHHyY8bJlxknP2ac\nfJlz8pPEjJO1wJQpU7Jhw4Y12rZixYrs61//enbkkUdmQ4YMyc4444xs/vz5jfZZt25d9vWvfz07\n5JBDshEjRmQXX3xxtnTp0kb7/POf/8y+/OUvZ8OGDcsOPfTQ7KqrrsrWrFnTkjKTcd9992Xl5eVZ\nRUVFVl5e3uinoqIiW7FiRVZfX5/deOON2eGHH54ddNBB2ec///ls0aJFjR5HfzdXTG+t3W1TW1ub\nffe7381Gjx6dDRo0KBs3blw2Z86chtut3ZYr1Ftrt/WcfPLJ2YQJExr+27ptXe/vb0deu2ac1mXG\nyY8ZJ39mnPyYcdqWOSc/HW3GKcmy931xOwAAAABJaZVr8AAAAADQfgQ8AAAAAIkT8AAAAAAkTsAD\nAAAAkDgBDwAAAEDiBDwAAAAAiRPwAAAAACROwAO0qV/+8pdRUVERzz//fLPuN2HChBgyZEhR+y5e\nvLglpQEAbBNzDtCeBDxAmxo5cmR897vfjb333rvZ9y0pKSm4z7333vt/7d1dSFTtGsbxyzE/GKOJ\nPogSMzvIqUHNMkVz1iQRWKSRUIOlBgWVQXgYHUUImSd9QGTZRMKUMkc14VnKFH1hjSIaWCdRUYIQ\nhikSps4+2LzD9nX57ra5lZn+PxCG28Vaz1oHw8X9PM8alZWVzWZoAAAAv4WcA2AhLVroAQD4s6Sk\npMwq9EhSKBT6r8cEg0GNjY3N6vwAAAC/g5wDYCGxggdA1PmVgAQAABCJyDkAZkKDB4Cpffv2ye12\nT6nV19fLbrfryZMn4drQ0JA2btyopqYmSVJLS4v27t2rjIwMGYahuro6jY6Oho8325ve39+vmpoa\n5ebmKi8vT7W1tfL5fLLb7erv758yhs7OTrndbmVlZamoqEgNDQ3hoFNZWakHDx5obGxMdrtd165d\nm+vHAgAAogA5B0A0YosWAFNOp1NNTU0aHR2V1WqVJL169UqS1NXVJZfLJUl6+fKlQqGQDMPQpUuX\ndOvWLZWUlKiyslLv379Xc3Ozent75fV6FRsbO+06w8PDqqio0PDwsI4cOaLExEQ1NzertbV12l70\n8fFxHT9+XAcOHFBZWZlaW1t19epVLV26VOXl5aqurlYoFFJ3d7fq6uqUnp7+f35KAAAgEpFzAEQj\nGjwATDmdTnk8HgWDQRmGoZGREfX19WnVqlXq7OwMH/fixQslJycrNjZWjY2NqqmpUXV1dfj/BQUF\nOnHihPx+v+lLAe/cuaP+/n75fD5lZWVJ+vesWnFx8bRjJycndebMGR08eFCSVFJSIpfLpba2NpWX\nl6ugoEAPHz5UT0+PSkpK5vqRAACAKEHOARCN2KIFwFR2drasVmt4Nquzs1MWi0WHDh1Sb2+vxsfH\nJUnPnz+XYRhqb2+XJO3YsUODg4Phv4yMDNlsNj1+/Nj0Ou3t7dq8eXM49EjSypUrVVpaarrHfM+e\nPeHPVqtVaWlp+vr161zdNgAA+AOQcwBEI1bwADAVHx+vvLw8dXR0SJI6OjrkcDhUUFCgy5cv682b\nN1q2bJm+fPkiwzDC+9X3799ver6BgQHT+qdPn7Rr165p9XXr1k2rxcXFafHixVNqCQkJGhkZ+V9u\nDQAA/OHIOQCiEQ0eADMqLCzUhQsXNDIyotevXys3N1cOh0NWq1XBYFBJSUmKi4tTfn6+AoGAJMnj\n8ZjuQU9KSjK9xsTEhOLi4qbVExISptX+vlcdAABgtsg5AKINDR4AM3I6nZqYmNDTp0/V19enU6dO\nyWKxKDs7W8FgUPHx8crNzVViYqJWr14tSUpOTlZaWtqU8zx69EgrVqwwvUZKSoo+fPgwrf7x48c5\nvx8AAIC/kHMARBvewQNgRmvXrlVqaqo8Ho8mJye1detWSdK2bdvU1dWljo4OOZ1OSVJRUZEkqbGx\ncco5AoGATp8+rba2NtNr7Ny5U93d3Xr79m24NjQ0ZPrrEr8ys2WxWDQ5OfnrNwkAAP5I5BwA0YYV\nPAD+UWFhoe7du6cNGzZoyZIlkqScnBxduXJFMTExMgxDkmS32+V2u+Xz+TQ4OCjDMDQwMCCv16vU\n1FQdPnzY9PzHjh2T3+9XVVWVqqqqZLVa5fP59P37d0lTw47Zywj/Xl++fLnGx8fV0NCg7du3KzMz\nc06eAwAAiD7kHADRhBU8AP7RXzNXOTk54VpmZqYSEhK0Zs0arV+/Plw/f/68zp49q8+fP+vixYvy\n+/3avXu3vF5vODRJU8OMzWbT3bt3tWXLFt2+fVs3b96Uy+VSRUWFQqFQeN96TEzMjDNb/1l3u93a\ntGmTrl+/rvv378/NQwAAAFGJnAMgmsSEZmoVA8A8+Pbtm2w2myyWqf3m2tpatbS0qKenR4sWsdgQ\nAABEHnIOgPnECh4AC6q+vl6GYejnz5/h2o8fPxQIBJSenk7oAQAAEYucA2A+8Y0CYEGVlpbK7/fr\n6NGjKi4u1sTEhPx+vwYGBnTu3LmFHh4AAMCskXMAzCe2aAFYcM+ePdONGzf07t07hUIhORwOnTx5\nUvn5+Qs9NAAAgN9CzgEwX2jwAAAAAAAARDjewQMAAAAAABDhaPAAAAAAAABEOBo8AAAAAAAAEY4G\nDwAAAAAAQISjwQMAAAAAABDh/gWhBCTM2Qp+ewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b398a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = sns.FacetGrid(col=\"sex\", data=df, size=8)\n",
    "g.map(plt.hist, \"weight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Samples vs population\n",
    "\n",
    "But we have never aked ourselves the philosophical question: what is data? **Frequentist statistics** is one answer to this philosophical question. It treats data as a **sample** from an existing **population**.\n",
    "\n",
    "This notion is probably clearest to you from elections, where some companies like Zogby or CNN take polls. The sample in these polls maybe a 1000 people, but they \"represent\" the electoral population at large. We attempt to draw inferences about how the population will vote based on these samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing a model\n",
    "\n",
    "Let us characterize our particular sample statistically then, using a *probability distribution*\n",
    "\n",
    "\n",
    "#### The Exponential Distribution\n",
    "\n",
    "The exponential distribution occurs naturally when describing the lengths of the inter-arrival times in a homogeneous Poisson process.\n",
    "\n",
    "It takes the form:\n",
    "$$\n",
    "f(x;\\lambda) = \\begin{cases}\n",
    "\\lambda e^{-\\lambda x} & x \\ge 0, \\\\\n",
    "0 & x < 0.\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "From Wikipedia: *In probability theory, a Poisson process is a stochastic process which counts the number of events and the time that these events occur in a given time interval. The time between each pair of consecutive events has an exponential distribution with parameter $\\lambda$ and each of these inter-arrival times is assumed to be independent of other inter-arrival times. The process is named after the French mathematician Siméon Denis Poisson and is a good model of radioactive decay, telephone calls and requests for a particular document on a web server, among many other phenomena.*\n",
    "\n",
    "In our example above, we have the arrival times of the babies. There is no reason to expect any specific clustering in time, so one could think of modelling the arrival of the babies via a poisson process.\n",
    "\n",
    "Furthermore, the Poisson distribution can be used to model the number of births each hour over the 24-hour period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109ab5190>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cJqxWq/7zP/9T+/btkyRdfPHFqqur086dO/XSSy/p9ttv11NPPeWpOgEAAACY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109966b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x, l: l*np.exp(-l*x)*(x>0)\n",
    "xpts=np.arange(-2,3,0.1)\n",
    "plt.plot(xpts,f(xpts, 2),'o');\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"exponential pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: **some of the code, and ALL of the visual style for the distribution plots below was shamelessly stolen from https://gist.github.com/mattions/6113437/ **."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3NL7jUd8J88a1KnEL/fr1w+zZszF37lyYmJiUuD4AiIiIQHp6OmrUqKEsc3Z2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sAAAG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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109cd05d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "\n",
    "x = np.linspace(0,4, 100)\n",
    "colors=sns.color_palette()\n",
    "\n",
    "lambda_ = [0.5, 1, 2, 4]\n",
    "plt.figure(figsize=(12,4))\n",
    "for l,c in zip(lambda_,colors):\n",
    "    plt.plot(x, expon.pdf(x, scale=1./l), lw=2, \n",
    "                color=c, label = \"$\\lambda = %.1f$\"%l)\n",
    "    plt.fill_between(x, expon.pdf(x, scale=1./l), color=c, alpha = .33)\n",
    "    \n",
    "plt.legend()\n",
    "plt.ylabel(\"PDF at $x$\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.title(\"Probability density function of an Exponential random variable;\\\n",
    " differing $\\lambda$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How would we draw from this distribution?\n",
    "\n",
    "Lets use the built in machinery in `scipy.stats`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qdQ7/pVavXq3nn39evXr10vTp00vs07ZtW40fP97hC0FBQYHatm2rF198sdTV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109ac3990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "plt.plot(xpts,expon.pdf(xpts, scale=1./2.),'o')\n",
    "plt.hist(expon.rvs(size=1000, scale=1./2.), normed=True, alpha=0.5, bins=30);\n",
    "plt.xlabel(\"x\")\n",
    "plt.title(\"exponential pdf and samples(normalized)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In `scipy.stats`, you can alternatively create a frozen object, which holds values of things like the scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z9O2332rdunUKCAjQAw88oGeeecbhoPCePXvKz89P8+fP17x581ShQgX17t1b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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e72c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rv = expon(scale=0.5)\n",
    "plt.plot(xpts,rv.pdf(xpts),'o')\n",
    "plt.hist(rv.rvs(size=1000), normed=True, alpha=0.5, bins=30);\n",
    "plt.plot(xpts, rv.cdf(xpts));\n",
    "plt.xlabel(\"x\")\n",
    "plt.title(\"exponential pdf, cdf and samples(normalized)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Understanding our data using a distribution\n",
    "\n",
    "Lets play with our data a bit to understand it:\n",
    "\n",
    "The first birth occurred at 0005, and the last birth in the 24-hour period at 2355. Thus the 43 inter-birth times happened over a 1430-minute period, giving a theoretical mean of 1430/43 = 33.26 minutes between births.\n",
    "\n",
    "Lets plot a histogram of the inter-birth times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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feeSR8a//+q/xX//1XzFy5MicTlZRUdH48YYNGyL2bsWkBbRt67bcvrO4A1RVVcWgQYPa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\nAACQCHEPAACJ+P/R+AndIt7VrAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b1b7450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "timediffs = df.minutes.diff()[1:]\n",
    "timediffs.hist(bins=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean or of an exponentially distributed random variable X with rate parameter $\\lambda$ can be analytically calculated as\n",
    "\n",
    "$$\\Ex[X] = \\frac{1}{\\lambda}.$$\n",
    "\n",
    "This makes intuitive sense: if you get babies at an average rate of 2 per hour, then you can expect to wait half an hour for every baby.\n",
    "\n",
    "The variance of X is given by\n",
    "\n",
    "$$\\Var[X] = \\frac{1}{\\lambda^2}.$$\n",
    "\n",
    "so the standard deviatiation is equal to the mean, just as in the discrete Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0300699300699 33.2558139535\n"
     ]
    }
   ],
   "source": [
    "lambda_from_mean = 1./timediffs.mean()\n",
    "print lambda_from_mean, 1./lambda_from_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAAYBrBAgAAAIBpBAsAAAAAphEsAAAAAJhGsAAAAABgGsECAAAAgGkECwAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a7a8a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minutes=np.arange(0, 160, 5)\n",
    "rv = expon(scale=1./lambda_from_mean)\n",
    "plt.plot(minutes,rv.pdf(minutes),'o')\n",
    "timediffs.hist(normed=True, alpha=0.5);\n",
    "plt.xlabel(\"minutes\");\n",
    "plt.title(\"Normalized data and model for estimated $\\hat{\\lambda}$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What did we just do? We made a 'point estimate' of the scale or rate parameter as a compression of our data. But what does it mean to make such a point estimate? The next section on **Frequentist Statistics** tells us. But first, lets see the Poisson Distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### An aside: The Poisson Distribution\n",
    "\n",
    "The *Poisson Distribution* is defined for all positive integers: \n",
    "\n",
    "$$P(Z=k)=\\frac{\\lambda^k e^{−\\lambda}}{k!}, k=0,1,2,... $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9AF+NfoDD/3ibooxM4+IpKuLuu+9m2rRphvSvZL4OubRuPkXrzYuIiEgNc2rV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\nCPBuj+lUQwsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b300fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import poisson\n",
    "k = np.arange(15)\n",
    "plt.figure(figsize=(12,8))\n",
    "for i, lambda_ in enumerate([1, 2, 4, 6]):\n",
    "    plt.plot(k, poisson.pmf(k, lambda_), '-o', label=lambda_, color=colors[i])\n",
    "    plt.fill_between(k, poisson.pmf(k, lambda_), color=colors[i], alpha=0.5)\n",
    "    plt.legend()\n",
    "plt.title(\"Poisson distribution\")\n",
    "plt.ylabel(\"PDF at $k$\")\n",
    "plt.xlabel(\"$k$\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "minutes\n",
       "0     1\n",
       "1     3\n",
       "2     1\n",
       "4     4\n",
       "7     2\n",
       "8     2\n",
       "9     1\n",
       "10    3\n",
       "11    1\n",
       "12    2\n",
       "13    1\n",
       "14    4\n",
       "15    1\n",
       "16    2\n",
       "17    1\n",
       "18    3\n",
       "19    4\n",
       "20    3\n",
       "21    2\n",
       "22    1\n",
       "23    2\n",
       "Name: minutes, dtype: int64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "per_hour = df.minutes // 60\n",
    "num_births_per_hour=df.groupby(per_hour).minutes.count()\n",
    "num_births_per_hour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0952380952380953"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_births_per_hour.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r187+397e3vLz81Pbtm3tbUFB5347e+bMGUnS7t271a9fP0myv7m9Y8eO8vf3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\n6keO4rXZAn2dXd10bttO57btoFKRPy2HhUWzUeW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zWZJeyoK0eYTozeN+SoSY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\njQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112947ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.arange(5)\n",
    "plt.figure(figsize=(12,8))\n",
    "tcount=num_births_per_hour.sum()\n",
    "plt.hist(num_births_per_hour, alpha=0.4,  lw=3, normed=True, label=\"normed hist\")\n",
    "sns.kdeplot(num_births_per_hour, label=\"kde\")\n",
    "plt.plot(k, poisson.pmf(k, num_births_per_hour.mean()), '-o',label=\"poisson\")\n",
    "plt.title(\"Baby births\")\n",
    "plt.xlabel(\"births per hour\")\n",
    "plt.ylabel(\"rate\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum Likelihood Estimation\n",
    "\n",
    "how did we know that the sample mean was a good thing to use?\n",
    "\n",
    "One of the techniques used to estimate such parameters in frequentist statistics is **maximum likelihood estimation**. Briefly, the idea behind it is:\n",
    "\n",
    "The product \n",
    "\n",
    "$$\n",
    "L(\\lambda) = \\prod_{i=1}^n P(x_i | \\lambda)\n",
    "$$\n",
    "\n",
    "gives us a measure of how likely it is to observe values $x_1,...,x_n$ given the parameters $\\lambda$. Maximum likelihood fitting consists of choosing the appropriate \"likelihood\" function $L=P(X|\\lambda)$ to maximize for a given set of observations. How likely are the observations if the model is true?\n",
    "\n",
    "Often it is easier and numerically more stable to maximise the log likelyhood:\n",
    "\n",
    "$$\n",
    "\\ell(\\lambda) = \\sum_{i=1}^n ln(P(x_i | \\lambda))\n",
    "$$\n",
    "\n",
    "In the case of the exponential distribution we have:\n",
    "\n",
    "$$\n",
    "\\ell(lambda) = \\sum_{i=1}^n ln(\\lambda e^{-\\lambda x_i}) = \\sum_{i=1}^n \\left( ln(\\lambda) - \\lambda x_i \\right).\n",
    "$$\n",
    "\n",
    "Maximizing this:\n",
    "\n",
    "$$\n",
    "\\frac{d \\ell}{d\\lambda} = \\frac{n}{\\lambda} - \\sum_{i=1}^n x_i = 0\n",
    "$$\n",
    "\n",
    "and thus:\n",
    "\n",
    "$$\n",
    "\\est{\\lambda_{MLE}} = \\frac{1}{n}\\sum_{i=1}^n x_i,\n",
    "$$\n",
    "\n",
    "which is identical to the simple estimator we used above. Usually one is not so lucky and one must use numerical optimization techniques.\n",
    "\n",
    "A crucial property is that, for many commonly occurring situations, maximum likelihood parameter estimators have an approximate normal distribution when n is large. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FREQUENTIST STATISTICS \n",
    "\n",
    "In frequentist statistics, the data we have in hand, is viewed as a **sample** from a population. So if we want to estimate some parameter of the population, like say the mean, we estimate it on the sample.\n",
    "\n",
    "This is because we've been given only one sample. Ideally we'd want to see the population, but we have no such luck.\n",
    "\n",
    "The parameter estimate is computed by applying an estimator $F$ to some data $D$, so $\\est{\\lambda} = F(D)$. \n",
    "\n",
    "\n",
    "**The parameter is viewed as fixed and the data as random, which is the exact opposite of the Bayesian approach which you will learn later in this class. **\n",
    "\n",
    "For the babies, lets assume that an exponential distribution is a good description of the baby arrival process. Then we consider some larger population of babies from which this sample is drawn, there is some true $\\trueval{\\lambda}$ which defines it. We dont know this. The best we can do to start with is to estimate  a lambda from the data set we have, which we denote $\\est{\\lambda}$. \n",
    "\n",
    "Now, imagine that I let you peek at the entire population in this way: I gave you some M data sets **drawn** from the population, and you can now find the mean on each such dataset, of which the one we have here is one.\n",
    "So, we'd have M means. You can think of these means as coming from some fixed parameter by some data drawing process\n",
    "\n",
    "Now if we had many replications of this data set: that is, data from other days, an **ensemble** of data sets, for example, we can compute other $\\est{\\lambda}$, and begin to construct the **sampling distribution** of $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Segue: many samples on the binomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats.distributions import bernoulli\n",
    "def throw_a_coin(n):\n",
    "    brv = bernoulli(0.5)\n",
    "    return brv.rvs(size=n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function below returns the mean for each sample in an ensemble of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_throws(number_of_samples, sample_size):\n",
    "    start=np.zeros((number_of_samples, sample_size), dtype=int)\n",
    "    for i in range(number_of_samples):\n",
    "        start[i,:]=throw_a_coin(sample_size)\n",
    "    return np.mean(start, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now do 200 replications, each of which has a sample size of 1000 flips, and store the 200 means for each sample zise from 1 to 1000 in `sample_means`. This will rake some time to run as I am doing it for 200 replications at 1000 different sample sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sample_sizes=np.arange(1,1001,1)\n",
    "sample_means = [make_throws(number_of_samples=200, sample_size=i) for i in sample_sizes]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So remember that for eachsample size, i am getting 200 means. Lets get the mean of the means at each sample size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mean_of_sample_means = [np.mean(means) for means in sample_means]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIqI4DDZU4Z/n/y0OPmYu2YtzlT6cOVeHBas4hzURERERkYz4Cza0zNGGUP7ZmujfxWXN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LG1NbQzkmVnWUKBLElIDfpx7bl1AGBIxtdaSFVFgxeDZ8NmzgbPrUgN+vHQynpAkrDo9v/F0fYG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\nryBsAAAAAPCK/wUcx6bVwz90agAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a9c8d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sample_sizes, mean_of_sample_means);\n",
    "plt.ylim([0.480,0.520]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not surprisingly, the mean of the sample means converges to the distribution mean as the sample size N gets very large.\n",
    "\n",
    "#### The notion of a Sampling Distribution\n",
    "\n",
    "(some text is quoted from Murphy's machine learning book)\n",
    "\n",
    "In data science, we are always interested in understanding the world from incomplete data, in other words from a sample or a few samples of a population at large. Our experience with the world tells us that even if we are able to repeat an experiment or process, we will get more or less different answers the next time. If all of the answers were very different each time, we would never be able to make any predictions.\n",
    "\n",
    "But some kind of answers differ only a little, especially as we get to larger sample sizes. So the important question then becomes one of the distribution of these quantities from sample to sample, also known as a **sampling distribution**. \n",
    "\n",
    "Since, in the real world, we see only one sample, this distribution helps us do **inference**, or figure the uncertainty of the estimates of quantities we are interested in. If we can somehow cook up samples just somewhat different from the one we were given, we can calculate quantities of interest, such as the mean on each one of these samples. By seeing how these means vary from one sample to the other, we can say how typical the mean in the sample we were given is, and whats the uncertainty range of this quantity. This is why the mean of the sample means is an interesting quantity; it characterizes the **sampling distribution of the mean**, or the distribution of sample means.\n",
    "\n",
    "So, in the babies case, the uncertainty in the parameter estimate can be measured by computing the **sampling distribution** of the estimator. \n",
    "What you are doing is sampling many Data Sets $D_i$ from the true population (which we are not given you will argue, and you are right, but just wait a bit), say M of them, each of size N, from some true model $p(\\cdot|\\trueval{\\lambda})$. We will now calculate M $\\est{\\lambda}_i$, one for each dataset. As we let $M \\rightarrow \\infty$, the distribution induced on $\\est{\\lambda}$ is the sampling distribution of the estimator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference \n",
    "\n",
    "Just having an estimate is no good. We will want to put confidence intervals on the estimation of the parameters. This presents a conundrum: we have access to only one sample, but want to compute a error estimate over multiple samples, using an estimator such as the standard deviation.\n",
    "\n",
    "At this point we are wishing for the Lord  to have given us those other samples drawn from the population that we talked about above. But alas, no such luck...\n",
    "\n",
    "In the last two decades, **resampling** the ONE dataset we have has become computationally feasible. Resampling involves making new samples from the observations, each of which is analysed in the same way as out original dataset. One way to do this is the Bootstrap. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrap\n",
    "\n",
    "Bootstrap tries to approximate our sampling distribution. If we knew the true parameters of the population, we could generate M fake datasets. Then we could compute the parameter (or another estimator) on each one of these, to get a empirical sampling distribution of the parameter or estimator, and which will give us an idea of how typical our sample is, and thus, how good our parameter estimations from our sample are.\n",
    "(again from murphy)\n",
    "\n",
    "But we dont have the true parameter. So we generate these samples, using the parameter we calculated. Or, alteratively, we sample with replacement the X from our original sample D, generating many fake datasets, and then compute the distribution on the parameters as before. \n",
    "\n",
    "We do it here for the mean of the time differences. We could also do it for its inverse, $\\lambda$.\n",
    "\n",
    "#### Non Parametric bootstrap\n",
    "\n",
    "Resample the data! We can then plot the distribution of the mean time-difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109966910>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aNNasWcNdd93F8uXL2bx5cxNdPWls6m4kIm1SujmRXHsmAAGWcLq69zW4ojJW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x104923710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M_samples=10000\n",
    "N_points = timediffs.shape[0]\n",
    "bs_np = np.random.choice(timediffs, size=(M_samples, N_points))\n",
    "sd_mean=np.mean(bs_np, axis=1)\n",
    "sd_std=np.std(bs_np, axis=1)\n",
    "plt.hist(sd_mean, bins=30, normed=True, alpha=0.5,label=\"samples\");\n",
    "sns.kdeplot(sd_mean, label=\"inferred distribution\")\n",
    "plt.axvline(timediffs.mean(), 0, 1, color='r', label='Our Sample')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Parametric Bootstrap\n",
    "\n",
    "And here we do it in a parametric way. We get an \"estimate\" of the parameter from our sample, and them use the exponential distribution to generate many datasets, and then fir the parameter on each one of those datasets. We can then plot the distribution of the mean time-difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10a96e550>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3eOLyQPrzKYvktDslSb8/vUf1LZcsrggAEE8ICQAGRZmnOLQ9gaFGA25Uwkgt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a779150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rv = expon(scale=1./lambda_from_mean)\n",
    "M_samples=10000\n",
    "N_points = timediffs.shape[0]\n",
    "bs_p = rv.rvs(size=(M_samples, N_points))\n",
    "sd_mean_p=np.mean(bs_p, axis=1)\n",
    "sd_std_p=np.std(bs_p, axis=1)\n",
    "plt.hist(sd_mean_p, bins=30, normed=True, alpha=0.5);\n",
    "sns.kdeplot(sd_mean_p);\n",
    "plt.axvline(timediffs.mean(), 0, 1, color='r', label='Our Sample')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
